Temperature dependence of the dielectric function of germanium

Abstract

Ellipsometric measurements of the dielectric constant of undoped Ge were performed between 1.25 and 5.6 eV in the temperature range of 100 to 850 K. The dependence of the ${E}_{1}$, ${E}_{1}+{\ensuremath{\Delta}}_{1}$, ${E}_{0}^{\ensuremath{'}}$, and ${E}_{2}$ critical energies on temperature was obtained. It can be represented either with Varshni's empirical formula or with an expression proportional to the Bose-Einstein statistical factor of an average phonon. Broadening parameters, amplitudes, and phase angles for the corresponding critical points were also obtained. A decrease of the excitonic interaction with increasing temperature was found. The results are discussed in the light of recent calculations of the effect of temperature on the band structure of Ge containing Debye-Waller and self-energy contributions.